Matthiessen-type decomposition of metallic resistivity Evaluate the statement: “The resistivity of metals consists of two parts, one approximately temperature independent (residual) and the other temperature dependent (e.g., phonon scattering).” Is this statement correct in practical engineering terms?

Introduction / Context:
Engineers often model metallic resistivity using Matthiessen’s rule, which separates contributions from different scattering mechanisms. Recognizing a residual (impurity/defect) term plus a temperature-dependent term (phonon scattering) is crucial for designing precision resistors, interconnects, and cryogenic instrumentation.

Given Data / Assumptions:

• Ordinary metals in their normal (non-superconducting) state.
• Temperature range not too close to phase transitions.
• Impurity and phonon scattering are the dominant mechanisms.

Concept / Approach:

Matthiessen’s rule states that total resistivity ρ(T) ≈ ρ_residual + ρ_lattice(T). The residual portion arises from static defects (impurities, dislocations, grain boundaries) and is weakly temperature dependent, while the lattice term grows with temperature due to increased electron–phonon scattering. Although exact additivity can break down under some conditions, the decomposition is widely useful and accurate for engineering calculations.

Step-by-Step Solution:

Verification / Alternative check:

Low-temperature data show ρ(T) saturating to a finite residual value; high-purity metals exhibit very small ρ0 and large residual-resistivity ratios (RRR), which validates the decomposition.

Why Other Options Are Wrong:

Saying “False” ignores well-established scattering physics; limiting it to 0 K or alloys only is unnecessarily restrictive; mentioning superconductors is irrelevant since their DC resistivity is zero below Tc.

Common Pitfalls:

Assuming perfect additivity at all temperatures and fields; in reality, deviations can occur, but the engineering statement remains correct.

Final Answer:

True